Final answer:
The largest acceptable error on a 1:20,000 scale map is 0.09 meters for 90% of well-defined points. The percent uncertainty of a measuring tape off by 0.50 cm over 20 m is 0.025%. Accuracy refers to closeness to the true value, while precision indicates the repeatability of measurements.
Step-by-step explanation:
The largest acceptable error for a map with a scale of 1:20,000, according to the National Map Accuracy Standards, would be 0.09 meters (or 9 cm) for 90% of well-defined points. This standard dictates that the error should not exceed 1/50th of an inch on the map, which translates to 0.02 inches. Since 1 inch on the map equals 20,000 inches in reality, we can calculate the largest acceptable error by multiplying 0.02 inches by 20,000 (the scale factor).
Percent uncertainty, in the context of a measuring tape, describes the ratio of the potential error to the total measurement distance. If a tape can be off by 0.50 cm over a distance of 20 m, its percent uncertainty is calculated by dividing the error by the total measurement distance and then multiplying by 100. The percent uncertainty would therefore be 0.50 cm / 2000 cm * 100%, which equals 0.025%.
Accuracy and precision are important concepts in measurements. Accuracy refers to how close a measurement is to the true value, whereas precision refers to how consistent and repeatable the measurements are. When discussing GPS systems, a system with low precision but high accuracy will have readings spread out but close to the true location, and a system with high precision but low accuracy will have readings that are closely clustered but far from the true location.